David Sweat (left) and Richard Matt have been on the run since June 6.New York State Police

Heavily armed police and bloodhounds are after escaped convicts Richard Matt and David Sweat — and so are rabid network news execs.

Sources tell Page Six there’s heated competition between bookers to be in position to land interviews with Matt and Sweat, if they’re captured, as the ratings war between network news divisions and their marquee morning shows heats up. Also in their cross hairs are Joyce Mitchell, the woman who allegedly helped the convicted killers, and her clueless husband, Lyle.

NBC’s already scored interviews with Joyce’s son and her ex-husband, but sources told us the network’s determined not to be scooped by ABC after Diane Sawyer first interviewed Caitlyn Jenner about her transition in April.

“After [Caitlyn] Jenner, NBC is worried that Diane Sawyer’s producers will get these convicts, too,” said a source. “NBC execs are still licking their wounds.” The source added NBC staffers have been joking they’ll “literally have to go find the renegades themselves.”

Meanwhile, an ABC insider crowed that its own producers “are all over it. ABC is chasing everybody involved” in the prison-break saga.

However, one TV insider downplayed the pressure: “This is definitely a big story, but it’s bigger in New York than it is across the country. I wouldn’t compare this to Caitlyn Jenner.”

Matt and Sweat were still on the run as of Monday, nine days after busting out of Clinton Correctional Facility. One question is whether the two would even be able to talk to the media. “It depends where they’re captured, and what laws and jurisdictions are there,” said a TV pro. “What if they’re in Canada? It all depends. There have been jailhouse interviews.” Tips have placed the dangerous duo everywhere from Vermont to Mexico.

An NBC rep said, “While others may dwell on bookings of the past, we’re focused on the present, like our exclusive with [former NAACP official] Rachel Dolezal Tuesday . . . Judging by our ratings momentum, that’s working for us.” ABC had no comment.